Monochromatic Electromagnetic Field Research Articles

On the Hilbert operator and the Hilbert formulas on the unit sphere for the time-harmonic Maxwell equations

In this work we establish some analogues of the Hilbert formulas on the unit sphere for the theory of time-harmonic (monochromatic) electromagnetic fields. Our formulas relate one of the components of the limit value of a time-harmonic electromagnetic field in the unit ball to the rest of components. The obtained results are based on the close relation between time-harmonic solutions of the Maxwell equations and the three-dimensional α-hyperholomorphic function theory. Hilbert formulas for α-hyperholomorphic function theory for α being a complex number are also obtained, such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit ball to the other pair of components, in an analogy with what happens in the case of the theory of functions of one complex variable.

Magnetoelectric effects in local light-matter interactions.

We study the generic dipole interaction of a monochromatic free-space electromagnetic field with a bi-isotropic nanoparticle or a molecule. Contributions associated with the breaking of dual, P, and T symmetries are responsible for electric-magnetic asymmetry, chirality, and the nonreciprocal magnetoelectric effect, respectively. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticle and introduce novel field characteristics quantifying the transfer of energy, momentum, and angular momentum due to the three symmetry-breaking effects. In particular, we put forward a concept of "magnetoelectric energy density," quantifying the local PT symmetry of the field. Akin to the "superchiral" light suggested recently for local probing of molecular chirality, here we suggest employing complex fields for a sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.

Tunneling ionization of atoms and ions in an elliptical electromagnetic wave and a static magnetic field

odinger equation and the Green’s function for an electron moving in an arbitrary electromagnetic wave and crossed constant electric and magnetic fields are obtained. The exact expressions are found for the level shift and width of the electron in a zero-range force field, a constant magnetic field, and a monochromatic electromagnetic field. In the case of ionization of neutral atoms and positive ions, we also take into consideration the Coulomb interaction of the emerging electron with the atomic or ionic core. The first-order contributions from the Stark and Zeeman effects to the ionization rate are taken into account as well. The paper generalizes the results earlier obtained by V. M. Rylyuk and J. Ortner [ Phys. Rev. A67, 013414 (2003)].

Modeling of the electrodynamic contact of two materials under the action of electromagnetic waves

A mathematical model of bilateral boundary conditions coupling monochromatic electromagnetic fields on both sides of the transition layer between two materials is developed. The field-induced double-layer surface charges and currents and complex surface capacitances and inductances of the transition region are taken into account. An analytic solution to the boundary value problem of penetration of an arbitrarily polarized plane electromagnetic wave through a two-layered screen with a transition plane region between the layers is obtained. The transmission and reflection coefficients for a plane wave are calculated.

Calculation of Electromagnetic Fields in Three Dimensions Using the Cauchy Integral

This paper describes a method for calculating the 3-D monochromatic electromagnetic fields scattered by conducting and dielectric objects using the Cauchy integral cast in a multidimensional form based on Clifford algebra. Formal relationships to methods based on quaternions and vector calculus are presented. The characteristics of solutions based on the Cauchy method are described and its advantages over comparable methods involving Greens functions are discussed.

Diffraction of Light by a Two-Dimensional Lattice of Spheres

Two-dimensional arrays of particles are of great interest because of their very characteristic optical properties and numerous potential applications. Although a variety of theoretical approaches are available for the description of their properties, methods that are accurate and convenient for computational procedures are always sought. In this work, a new technique to study the diffraction of a monochromatic electromagnetic field by a two-dimensional lattice of spheres is presented. The method, based on Fourier series, can take into account an arbitrary number of terms in the multipole expansion of the field scattered by each sphere. This method has the advantage of leading to simple formulas that can be readily programmed and used as a powerful tool for nanostructure characterization.

Laser control of low-temperature reaction e − + O 2 +

A theory is developed to describe dissociative recombination of a slow electron with a ground-state molecular ion of oxygen driven by a strong monochromatic electromagnetic field. Mathematically, the theory is based on the time-independent formalism of radiative scattering matrix whose poles correspond to dressed intermediate states of the complex. The analysis embraces both transitions to dissociative states and laserinduced nonadiabatic transitions to intermediate bound states of valence configurations. Key reaction mechanisms are considered, and a classification is given of all allowed transitions to dissociative states. Partial and total reaction cross sections are calculated by taking into account the contributions from Rydberg, valence, and dissociative states of O2**. A detailed discussion of results is presented, and feasibility of laser control of the reaction is demonstrated.

Photocurrent in a visible-light graphene photodiode

We calculate the photocurrent in a clean graphene sample normally irradiated by a monochromatic electromagnetic field and subject to a step-like electrostatic potential. We consider the photon energies $\hbar\Omega$ that significantly exceed the height of the potential barrier, as is the case in the recent experiments with graphene-based photodetectors. The photocurrent comes from the resonant absorption of photons by electrons and decreases with increasing ratio $\hbar\Omega/U_0$. It is weakly affected by the background gate voltage and depends on the light polarization as $\propto\sin^2\gamma$, $\gamma$ being the angle between the potential and the polarization plane.

Simulation of monochromatic and pulse electromagnetic fields in a spherical layered structure

Rigorous analytic methods of electromagnetics are applied to develop a mathematical model for calculation of monochromatic and pulse electromagnetic fields in a sphere enclosed in a shell with arbitrary permittivity and permeability. The influence of the shell and of the position of the reception point located in a spherical single-layer structure on the transmitted pulse electromagnetic field is investigated numerically. Possible applications of the proposed model are indicated.

Free-space asymptotic far-field series

A systematic procedure for deriving the complete asymptotic series in inverse powers of the distance from the origin of free-space 2D and 3D, scalar and vectorial, monochromatic electromagnetic fields is derived here. Each term of the series is expressed in closed form through the use of a differential operator acting on the angular spectrum. A simple recursive routine for computing the derivatives is provided. Examples of application are also given.

Electron bunch interaction with a monochromatic electromagnetic wave

A technique of modulation of the charge density in a bunch when it interacts with a linearly polarized laser beam is developed. Solution of the problem is based on the numerical method for determination of interaction time of different electrons in the bunch flying through the interaction region, with use of an integral of motion of an electron in the monochromatic electromagnetic field. It is shown that in the terahertz frequency range, at high values of the field strength, sufficiently harddriving modulation of the charge density in the bunch may be obtained. High efficiency of the bunch charge density modulation is demonstrated in plots for different electrodynamical parameters.

On Electromagnetic-Acoustic Analogies in Energetic Relations for Waves Interacting with Material Surfaces

In the paper we consider propagation of a monochromatic surface electromagnetic field at the interface separating two semi-infinite media — a metamaterial (generally with complex permittivity and permeability) and a conventional dielectric medium. The metamaterial is treated as homogeneous and isotropic (it is so-called effective medium approximation). It is true for e.g. artificial metamaterials with negative dielectric permittivity and negative permeability in the microwave frequency range. The last materials are known as left handed and a conventional as right handed media. In this work the classical optical theorem is extended to the case of scattering of electromagnetic surface waves incident at the interface separating a left handed medium and a right handed dielectric medium. The analogous theorem is known in the scattering theory for elastic fields.

INTERSUBBAND TRANSITIONS IN COUPLED QUANTUM WELLS UNDER AN INTENSE LASER FIELD

We consider the electrons bound in the conduction band of a double quantum well interacting with a strong monochromatic electromagnetic field in the terahertz (THz) region. Using a variant of the stationary perturbation theory, we have obtained the quasienergies and Floquet eigenvectors. The main features of power broadening and the dynamic Stark shift are retained. The sensitivity to the field parameters, such as intensity and frequency of the electric field on the state populations, can be used in various optical semiconductor device applications.

Monochromatic electromagnetic fields with maximum focal energy density

The monochromatic electromagnetic fields that achieve maximum focal energy density for a given input power and directional spread are found through a variational approach. It is found that the polarization of the fields at the focal point must be perpendicular to the main direction of propagation. Parametric expressions relating the directional spread and focal energy density of these fields (and others that achieve stationary focal irradiance) are found, both in the optical (electric field only) and in the electromagnetic cases.

Laser modified processes: bremsstrahlung and inelastic photon–atom scattering

We consider the influence of a low-frequency monochromatic external electromagnetic field (the laser) on two basic atomic processes: electron Coulomb bremsstrahlung and inelastic photon scattering on an electron bound in the ground state of a hydrogenic atom. We briefly describe the approximations adopted and illustrate in figures how the laser parameters modify the shape of the differential cross-sections and extend the energy domain for emitted electrons, due to simultaneous absorption or emission of a large number (hundreds) of laser photons.

Floquet solutions for two-dimensional quasi-free electrons interacting with a monochromatic laser field

We consider quasi-free electrons, moving in a two-dimensional lattice, and interacting with a strong monochromatic electromagnetic field; the interaction between each electron and the lattice is considered to be sufficiently weak, so it is possible to treat it as a small perturbation. Using a variant of the stationary perturbation theory in the extended Hilbert space, we have obtained the quasi-energies and the reduced Floquet eigenvectors of a quasi-free electron. The low order perturbation corrections show that the quasi-energy spectra have positive and negative jumps and the Floquet eigenfunctions have generalized Bloch form. These results show some similarities to the corresponding properties of the conservative quasi-free electron model, in the absence of the external radiation field.

Homogenization of a Wire Photonic Crystal: The Case of Small Volume Fraction

We consider the diffraction of a monochromatic incident electromagnetic field by a bounded obstacle made of parallel high conducting metallic fibers of finite length which are periodically disposed. Our goal is to study the asymptotics of this three‐dimensional Maxwell problem as the period, the thickness of the rods, and the resistivity are simultaneously small. We solve this problem in the case where the filling ratio of fibers vanishes but their capacity remains positive. We find a limit volumic density of current which results in a nonlocal constitutive relation between the electric and displacement fields. This extends previous results obtained in the polarized case where a two‐dimensional effective local equation was found with a possibly negative effective permittivity.

Nonunitary squeezing and biorthogonal scalar products in polarization optics

The polarization vectors of monochromatic electromagnetic fields can be transformed by multiplying them by 2 ? 2 matrices representing, respectively, retardation plates, rotators and partial polarizers. The present description of partial polarizers is related to a two-dimensional Lorentz algebra SU(1,1) leading to nonunitary squeezing as the present SU(1,1) algebra includes non-Hermitian operators in addition to the Hermitian ones. The present analysis exploits the use of similarity transformations which are more general than the unitary transformations used usually in quantum mechanics. By performing a similarity transformation on a set of Hermitian physical operators the transformed operators are Hermitian with respect to new scalar product defined by the use of a new metric. It is shown that such transformations can be implemented experimentally by the use of polarization optics and the metric obtained in such transformations is analysed.

Microscopic models of quantum-jump superoperators

We discuss the quantum jump operation in an open system, and show that jump super-operators related to a system under measurement can be derived from the interaction of that system with a quantum measurement apparatus. We give two examples for the interaction of a monochromatic electromagnetic field in a cavity (the system) with 2-level atoms and with a harmonic oscillator (representing two different kinds of detectors). We show that derived quantum jump super-operators have `nonlinear' form which depends on assumptions made about the interaction between the system and the detector. A continuous transition to the standard Srinivas--Davies form of the quantum jump super-operatoris shown.

Time-dependent entropy of simple quantum model systems

Information-theoretic entropy measures are useful tools for quantifying the spreading of quantum states in phase space. In the present paper, we compare the time evolution of the joint entropy for three simple quantum systems: (i) a free Gaussian wave packet, (ii) a wave packet in a monochromatic electromagnetic field, and (iii) a wave packet tunneling through a $\ensuremath{\delta}$ barrier. As initial condition maximal classical states are used, which minimize the Heisenberg uncertainty and the entropy. It is found that, in all three cases, the joint entropy increases in time.